Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + Relative maximum: (2, 9)…

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Q: 2. Solve the outgoing signal problem Utt- c²uxx=0, x > 0, -∞ <t<∞o; ux(0,t) = s(t), -∞ <t<∞, where…

A: From the given details above we have,

Q: 3. Josephine is purchasing a used car. Her bank has offered a loan of $5000 at 5%/a compounded…

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Q: : r= = (2,0) + s(-3,-3) determine if land l₂ will intersect or not. 20. Given l₁ : r = (1, -2,) +…

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Q: A is an m x p matrix, B is a p x k matrix, and C is a k x n matrix. Show that A or (B or C) = (A or…

A: Introduction: Matrix multiplication is divided into two types: Scalar Matrix Multiplication, in…

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A: Given: Four playing boys marbles and their names have given.

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A: Here we can use general expension.

Q: 3- Let a: (F(R), +..) → (R, +..) be the map defined by a(f) = f(3)-f(0). Then o is a ring…

A: Given: σ:Fℝ, +, ·→ℝ, +, · be the mapping defined by, σf=f(3)-f(0) To determine: Whether σ is a ring…

Q: Q3A)Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A: We have to solve given problems:

Q: Solve the problem. Let T: 2->2 be a linear transformation that maps u = Use the fact that T is…

A: Given , T(u)=(7,-8) i.e. T(4,5)=(7,-8) And T(v)=(7,-4) i.e. T(2,-1)=(7,-4) Now ,we have find image…

Q: -sin20 B)Evaluate the integrals: i) f/2 sinze rdrde, 0 ii) f/2/2 finx 2² siny dz dy dx. 0 0

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Q: A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table.…

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-an and n…

Q: Find the general solutions of the system. 30-4 4# -15 -1 x 10 7 x(t) =

A: We solve given system by eigenvalues and eigenvectors.

Q: Show that A(1,0,2), B(-1,2,7), C(4,0,1) & D(2, -2,-3) are non- coplanar.

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Q: Write each of the following sets in correct roster notation: (a) {n % 5 : x ∈ N} (b) {x ∈ N : x 2 ≤…

A: (a) Given set is ={x%5:x∈N} The elements of the set are remainders obtained by dividing by 5. So,…

Q: quares and equilateral triangles can form a tiling that has at every vertex: O A. one square and…

A: We will use the fact that the angles at any vertex in tiling must add to 360°.

Q: Question 71 Determine the most suitable form of M) that should be used when solving each 24 ...)…

A: a. The given differential equation is y''+9y=sin2t+t2cos3t+3........(1) To find: the solution of the…

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Q: - Group 2. Santillan, Marken M. Gonzales, Kent Tibon, Clarence Variable Separable Set-A: Module 2 =…

A: Group 2. - Santillon, Marken M. - Gonzales, Kent -Tibon, Clarence…

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A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: 2. A water treatment plant processes gray water at a rate given by r(t) = 16e0.2 million gallons per…

A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q2)…

Q: Apply Gauss's theorem to evaluate. r.^ frds or ff. n.V(!) ds or ff - () ds Ən where S is any closed…

A: Given  ∫∫Sr.n^r3ds where S is any closed surface. By Gauss-divergence theorem,  ∫∫Sr.n^r3ds=∫∫v∫…

Q: Solve the following simultaneous linear D.E. 4 [2D [2D+1 D+ D-4 11 {} D+3)=(e) -

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Q: Question # 1: Part: a:For given matrix A, find Col(A), Row(A) and Null(A). Also write the dimension…

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Q: Evaluate f x²+8x+15 dx by using the integration by partial fraction.

A: We will factorize the denominator and then separate hose factors by using partial fraction method.…

Q: . Find the acute angle between the line joining A(1,2,3) and and the plane containing point…

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Q: B)Solve differential equation = (x+y) dx x+siny

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Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10…

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Q: 7. Lucas does not like Dustin weapon and decides to design his own. His model has a plane that…

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Q: Determine the length of the third side of the right triangle. Write the answer as a simplified…

A: Pythagorean theorem:  The square of length of hypotenuse is sum of square of length of other sides…

Q: Show the surface area and volume of a sphere with radius r is 4nr² and πr-³ respectively.

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A: Given that Profit ton of the interior paint is 4 thousands dollars and the profit per ton of…

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Q: The base of a three-dimensional figure is bound by the line y = -x + 1 on the interval [-3, 0].…

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Q: simplification is to isolate terms and identify the dominant term. For instance, we might want to…

A: fx(n) =log2log2n+3for n→∞log2n+3 =log2n

Q: 4) 4 6 9 0 0 5 3 -3 2 -2 X2 01 X3 5- 0 = 44 66 124

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Q: b) (D² +₁²) x = a sin(n+ +2), where x= D X = O X=DX = 0 at t=0

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Q: B)Convert r = √2 cos(0-7) = √2 cos(0-) to cartesian.

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Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

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Q: ГО 0 01 = 0 1 4 Lo 2 3] a) Find the eigenvalues of A. b) Find a nonsingular matrix P and a diagonal…

A: The given problem is to find the eigenvalues and eigenvectors of the given matrix and also find the…

Q: What is REF of C? [1 4 L7 C = I -31 -8 0

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Q: Q (x) 400, Use the graph of f'(x) to discuss the graph of y = f(x). Organize your conclusions in a…

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Q: 10 D+21 [D+3D+3] {x} = {2}

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Q: Show the surface area and volume of a sphere with radius r is 47r² and ³ respectively.

A: Let us derive the surface area and the volume of the sphere of radius r with integral calculus in…

Q: 8. Show that 4 29! +5! is divisible by 31.

A: We have to prove that 4.29!+5! is divisible by 31.

Q: 14.a) Use the Gram Schmidt Orthogonalization Procedure to transform the basis {(0, 1, 2), (1, 1, 2),…

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Q: Find the solution of the given initial value problem. 3y"" + 72y' 480y = 0; y (0) = 9, y'(0) = 24,…

A: Solution:

Q: S Js V is the volume enclosed x (axr)ds = 2aV, where a by the closed surface S.

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Q: A restaurant borrows $15,700 from a local bank for 7 months. The local bank charges simple interest…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - 3y' - 18y = 0,…

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